class sknano.core.geometric_regions.Parallelogram(o=None, u=None, v=None)[source][source]

Geometric2DRegion for a parallelogram.

New in version 0.3.0.

Represents a parallelogram with origin \(o=(o_x, o_y)\) and direction vectors \(\mathbf{u}=(u_x, u_y)\) and \(\mathbf{v}=(v_x, v_y)\).


o : array_like, optional

Parallelogram origin. If None, it defaults to o=[0, 0].

u, v : array_like, optional

Parallelogram direction vectors stemming from origin o. If None, then the default values are u=[1, 0] and v=[1, 1].


Parallelogram represents the bounded region \(\left \{o+\lambda_1\mathbf{u}+\lambda_2\mathbf{v}\in R^2 |0\le\lambda_i\le 1\right\}\), where \(\mathbf{u}\) and \(\mathbf{v}\) have to be linearly independent.

Calling Paralleogram with no parameters is equivalent to Parallelogram(o=[0, 0], u=[1, 0], v=[1, 1])


area Paralleogram area, \(A=|\mathbf{u}\times\mathbf{v}|\).
center Alias for centroid.
centroid Paralleogram centroid, \((c_x, c_y)\).
fmtstr Format string.
measure Alias for area, which is the measure of a 2D geometric region.
o 2D point coordinates \((o_x, o_y)\) of origin.
u 2D direction vector \(\mathbf{u}=(u_x, u_y)\), with origin o
v 2D direction vector \(\mathbf{v}=(v_x, v_y)\), with origin o


center_centroid() Center centroid on origin.
contains(point) Test region membership of point in Parallelogram.
rotate([angle, axis, anchor_point, ...]) Rotate GeometricRegion points and vectors.
todict() Returns a dict of the Paralleogram constructor parameters.
translate(t[, fix_anchor_points]) Translate GeometricRegion points and vectors by Vector t.